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Positive Definite Completions and Continuous Graphical Models

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Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

Daniel Kuhn, Viet Anh Nguyen, Peyman Mohajerin Esfahani

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst ...

2020

The chapter presents an approach for the interactive definition of curves and motion paths based on Gaussian mixture model (GMM) and optimal control. The input of our method is a mixture of multivariate Gaussians defined by the user, whose centers define a ...

Springer2019

Covariance operators play a fundamental role in functional data analysis, providing the canonical means to analyse functional variation via the celebrated Karhunen-Loève expansion. These operators may themselves be subject to variation, for instance in con ...

EPFL2019

Recovering covariance from functional fragments

Victor Panaretos, Marie-Hélène Descary

We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is observed only on a subinterval of length , one has no statistical information on ...

2019

Pairwise Comparisons with Flexible Time-Dynamics

Matthias Grossglauser, Lucas Maystre, Victor Kristof

Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We achieve this by replac ...

ASSOC COMPUTING MACHINERY2019

Stationary time-vertex signal processing

Nathanaël Perraudin, Andreas Loukas

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some known graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that g ...

2019

Functional data analysis by matrix completion

Marie-Hélène Descary

Traditional approaches to analysing functional data typically follow a two-step procedure, consisting in first smoothing and then carrying out a functional principal component analysis. The idea underlying this procedure is that functional data are well ap ...

EPFL2017

Gaussian Mixture Regression on Symmetric Positive Definite Matrices Manifolds: Application to Wrist Motion Estimation with sEMG

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

In many sensing and control applications, data are represented in the form of symmetric positive definite (SPD) matrices. Considering the underlying geometry of this data space can be beneficial in many robotics applications. In this paper, we present an e ...

2017

A Prediction-Error Covariance Estimator for Adaptive Kalman Filtering in Step-Varying Processes: Application to Power-System State Estimation

Jean-Yves Le Boudec, Mario Paolone, Lorenzo Zanni

In this paper, we present a new method for the estimation of the prediction-error covariances of a Kalman filter (KF), which is suitable for step-varying processes. The method uses a series of past innovations (i.e., the difference between the upcoming mea ...

Institute of Electrical and Electronics Engineers2017

We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The deriv ...

Pergamon-Elsevier Science Ltd2017